An Ostrogradsky Instability Analysis of Non-minimally Coupled Weyl Connection Gravity Theories

Abstract

We study the Hamiltonian formalism of the non-minimally coupled Weyl connection gravity (NMCWCG) in order to check whether Ostrogradsky instabilities are present. The Hamiltonian of the NMCWCG theories is obtained by foliating space-time into a real line (representing time) and \mbox{3-dimensional} space-like hypersurfaces, and by considering the spatial metric and the extrinsic curvature of the hypersurfaces as the canonical coordinates of the theory. Given the fact that the theory we study contains an additional dynamical vector field compared to the usual NMC models, which do not have Ostrogradsky instabilities, we are able to construct an effective theory without these instabilities, by constraining this Weyl field.

arXiv comment7 pages

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Cited by in corpus (6)

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• Black Hole Solutions in Non-Minimally Coupled Weyl Connection Gravity
• The non-minimally coupled symmetric teleparallel gravity with electromagnetic field
• On Scalar Cosmological Perturbations in Non-Minimally Coupled Weyl Connection Gravity
• Weak Field Limit of the Nonminimally Coupled Weyl Connection Gravity
• Black hole shadows in nonminimally coupled Weyl connection gravity